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Unformatted text preview: Chapter 4 T Puzzle A classic puzzle demonstrates complex arithmetic. Figure 4.1. The wooden T puzzle. Photo courtesy of Shop New Zeland, http://www.shopnewzealand.co.nz . I first saw the wooden T puzzle shown in figure 4.1 at Puzzling World in Copyright c 2009 Cleve Moler Matlab R is a registered trademark of The MathWorks, Inc. TM August 8, 2009 1 2 Chapter 4. T Puzzle Wanaka, New Zealand. They told me that it was their most popular puzzle. I have since learned that it was a well-known toy in the 1800s and an advertising tool in the early 1900s. The underlying mathematics involves geometry, trigonometry, and arithmetic with complex numbers. The t_puzzle program in the exm toolbox demonstrates some useful programming techniques. Figure 4.2. The four pieces. Figure 4.2 shows the electronic version of the four pieces. They all have the same width, but different heights. One of them has an unshapely chunk cut out of it, resulting in an irregular pentagon. Figure 4.3. The T. It turns out to be possible to arrange the four pieces to form the capital “T” shape shown in figure 4.3, as well as the arrow and the rhombus shapes shown in figure 4.4. What happened to those all of those 45 ◦ angles and what happened to that chunk? If you do a Google search on “T-puzzle” you can quickly see how to solve the puzzle and form the T, but please try t_puzzle for a while before you go surfing for the solution. If you click near the center of one of the four pieces, you can move 3 Figure 4.4. The arrow and the rhombus. it horizontally and vertically. If you click near one of the vertices, you can rotate a piece about its center. If you click with the right mouse button, or, on a one- button mouse, hold down the control key while you click, you can flip a piece over horizontally, changing its right/left-handed orientation. If you click in the subplothorizontally, changing its right/left-handed orientation....
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